MATHEMATICS COLLEGE

Use the product rule to calculate the derivatives of
( ax² + bx + c ) ( cx + d )

Answers

Answer 1

Answer:

$\n \sf\longmapsto (d)/(dx)(ax^2+bx+c)(cx+d)$

$\boxed{\sf (d)/(dx)f(x).g(x)=f(x)(d)/(dx)g(x)+g(x)(d)/(dx)f(x)}$

c and d are constants

$\n \sf\longmapsto (ax^2+bx+c)(d)/(dx)(cx+d)+(cx+d)(d)/(dx)(ax^2+bx+c)$

$\n \sf\longmapsto (ax^2+bx+c)(c)+(cx+d)(2ax+b)$

$\n \sf\longmapsto acx^2+bcx+c^2+2acx^2+bcx+2adx+bd$

$\n \sf\longmapsto 3acx^2+2bcx+2adx+bd+c^2$

Answer 2

Answer:

Answer:

• Product rule is as below:

${ \boxed{ \tt{ \: (dy)/(dx) = { \huge{v}} (du)/(dx) + { \huge{u}} (dv)/(dx) }}} \n$

u is (ax² + bx + c)
v is (cx + d)
du/dx is 2ax + bx
dv/dx is c

$\hookrightarrow \: { \rm{ (dy)/(dx) = (cx + d)(2ax + b) + (ax {}^(2) + bx + c)(c) }} \n \n { \rm{ (dy)/(dx) = (2ac {x}^(2) + bcx + 2adx + db) + (ac {x}^(2) + bcx + {c}^(2) )}} \n \n { \boxed{ \rm{ (dy)/(dx) = 3ac {x}^(2) + \{2bcx + 2adx \}x + (db + {c}^(2)) }}}$

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A total of 707
tickets were sold for the school play. They were either adult tickets or student tickets. There were
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more student tickets sold than adult tickets. How many adult tickets were sold?

Answers

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The number line below represents which combined inequality?number line with a closed circle on negative 4 and 3 with shading in between

x greater than or equal to −4 and x less than or equal to 3
x greater than or equal to −4 or x less than or equal to 3
x less than or equal to −4 and x greater than or equal to 3
x less than or equal to −4 or x greater than or equal to 3

Answers

x greater than or equal to −4 and x less than or equal to 3

This is because of the fact that it is in between.

Answer:

Step-by-step explanation:

X greater or equal to -4 and X less than or equal to 3

Answer number one

GEOMETRY QUESTION, URGENT!The volume V of a right circular cylinder is given by the formula V=πr²h, where r is the radius and h is the height.
A. Solve formula for h
B. Find the height of a right circular cylinder whose volume is 72π cubic inches and whose radius is 6 inches.

Answers

A.) $v/ \pi r=h$
B.) $h=2$

Find the missing angles in the Parallelogram

Answers

Explanation:

On the first pass, you know ...

g = 80° . . . vertical angles
I = 110° . . . vertical angles
m = 20° . . . alternate interior angles (WX║ZY)

Then on the second pass, you can figure ...

f = h = 180° -80° = 100° . . . linear angles
j = k = 180° -110° = 70° . . . linear angles
b = n = 180° -110° -m = 50° . . . sum of angles of a triangle

And the remaining angles can be determined using external angle and sum-of-angle relationships.

a = o = h -70° = 30°
c = 80° -b = 30°
d = 360° -80° -20° -I = 150°
L = c - m = 10° . . . c and L+m are alternate interior angles
e = L +70° or 110° - o = 80°

What is the base 10 representation of 11102?

Answers

Answer:

Step-by-step explanation:

The base two number one one one zero is equal to one times eight, plus one times four, plus one times two, plus zero times one, which simplifies to fourteen.

Answer:

1.1102 * 10^4

Step-by-step explanation:

11102

= 1.1102 * 10^4

Finding the work done in stretching or compressing a spring. Hooke's Law for Springs.
According to Hooke's law, the force required to compress or stretch a spring from an equilibrium position is given by F(x)=kx, for some constant k. The value of k (measured in force units per unit length) depends on the physical characteristics of the spring. The constant k is called the spring constant and is always positive.

In this problem we assume that the force applied doesn't distort the metal in the spring.

A 2 m spring requires 11 J to stretch to 2.4 m. Find the force function, F(x), for the spring described.

Answers

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached images below to see the step by step explanation to the question above.

Final answer:

To find the force function of a spring using Hooke's Law, you first identify the spring constant 'k' using the given work done and extension. In this case, we found 'k' to be 137.5 N/m. Hence, the force function F(x) for the spring comes out to be 137.5x N.

Explanation:

The problem revolves around Hooke's Law, which is used to determine the force needed to stretch or compress a spring by a certain distance away from its equilibrium position. This law can be mathematically represented as F(x)=kx, where 'F(x)' represents the force applied, 'k' is the spring constant, and 'x' is the distance.

In this question, the work done (W) to stretch the spring is given as 11 J, and the extension (Δx) is 0.4 m (from 2 m to 2.4 m). The work done on a spring is calculated by the equation W = 1/2 * k * (Δx)^2. From this, you can solve for 'k' value. Once you have 'k', you can find the force function F(x) for the spring.

1. Calculate 'k' using the work done equation:

11 J = 1/2 * k * (0.4 m)^2 ➔ k = 137.5 N/m

2. Substitute 'k' in F(x):

F(x) = 137.5 N/m * x

Hence, the force function F(x) = 137.5x N is required to extend the spring by 'x' metres.